CORRECT HYDROGEN MOLECULE
By Prof. L. Kaliambos (Natural Philosopher in New Energy) September 4, 2015 It is well known that in 1913 Bohr using the correct quanta of energy E = hν ( Planck 1900) and applying the electric force of the well-established law of Coulomb (1785) developed his successful model for describing the proton-electron interaction. Later Schrodinger (1926) after the discovery of the wave nature of electron developed the so-called Quantum Mechanics. Despite the enormous success of the Bohr model and the Schrodinger equation based on the well-established electromagnetic laws in explaining the principal features of the spectrum of one-electron atomic systems, neither was able to provide a satisfactory explanation of the chemical properties of atoms for forming molecules, because the discovery of the electron spin gives a peripheral velocity greater than the speed of light which is in contradiction with Einstein's accepted theory of relativity. Therefore under the influence of the invalid relativity physicists like Heisenberg, Pauli, and Dirac, developed qualitative approaches of the so-called qualitative symmetric properties including not the real magnetic and electric interactions between the two electrons of opposite spin . Moreover after the discovery of the assumed uncharged neutron (1932) nuclear physicists abandoned the well-established laws of electromagnetism in favor of wrong theories which could not lead to the nuclear structure. Under this crisis of physics I published my papers “Nuclear structure is governed by the fundamental laws of electromagnetism" (2003) and “ Spin-spin interactions of electrons and also of nucleons create atomic molecular and nuclear structures”(2008). Note that velocities faster than the speed of light give magnetic attractions of short range which overcome the electric repulsions of long range at short inter-electron separations. (See my FASTER THAN LIGHT). It is well known that in 1925 Goudsmit and Uhlenbeck discovered the electron spin S = s(s+1)0.5 (h/2π) where s = 1/2 which gives a peripheral velocity u greater than the speed of light (u >> c ) invalidating Einstein’s relativity (EXPERIMENTS REJECT RELATIVITY). In fact, I discovered that the velocity (u >>c ) cannot be related with the absorption of photons in the CORRECT EXPLANATION OF PHOTOELECTRIC EFFECT . Such a velocity (u >> c ) gives stronger magnetic attraction than the electric repulsion at an inter-electron separation r < 578.8/1015 m. So in the absence of such a detailed knowledge, great theoretical physicists, under the strong influence of the invalid relativity, abandoned the natural laws of electromagnetism and developed theories with qualitative approaches. Following the work, of Pauli (1925) who suggested the qualitative exclusion principle for two electrons of opposite spin, Heisenberg inroduced the hypothesis of the so-called exchange interaction. Then chemists studied the chemical properties of numerous compounds. Though their efforts shed much light on the subject, the fundamental nature of the forces that hold atoms together to form the simplest hydrogen molecule remained mysterious. For example about 1927 great scientists like Heitler, London, Born, Oppenheimer, and later, Pauling, and others, under the abandonment of natural laws of electromagnetism applied without success the new techniques of the quantum mechanics to the problem. Under such a crisis a new Molecular Orbital Theory was developed in the years after the qualitative valence bond (1927) primarily through the efforts of Hund and Muliken. In the Molecular Orbital Theory, atoms form bonds by sharing electrons. That is, in the absence of a real attractive force atomic orbitals combine theoretically to form molecular orbitals. Similar to atomic orbitals, molecular orbitals were assumed to be wave functions giving the probability of finding an electron in certain regions of a molecule. Each molecular orbital can only have 2 electrons, each with an opposite spin. The hydrogen molecule for example was assumed to have two molecular orbitals, an antibonding orbital and a bonding orbital. However the theory cannot explain how the atomic orbitals overlap, to give an increase in electron density and therefore an increase in the intensity of the negative charge. In fact an attractive magnetic force contributes to the increase in negative charge which causes the nuclei to be drawn closer together. Due to the lower potential energy in molecular bonds than in separate atomic orbitals, it is more energy efficient for the electrons to stay in a molecular bond rather than be pushed back into the 1s orbitals of separate atoms. This is what keeps bonds from breaking apart. However in the absence of such a detailed knowledge today the Molecular Orbital Theory is applied in a manner using sum empirically derived parameters. DISCOVERY OF THE BINDING ENERGY OF THE SIMPLE HYDROGEN MOLECULE Here the two electrons of opposite spin (S = 0) behave like one particle circulating about the two separated nuclei with opposite spin under the rules of quantum mechanics. In this bonding state we neglect the very small magnetic attraction between the two spinning protons of opposite spin. If the protons are well separated the system of two electrons with S =0 will be bound to one or the other. The ground state energy in eV in each proton is then given by E = -27.2 Z2 + 16.95 Z -4.1 eV. Since Z=1 one gets E = -14.35 eV As the proton-proton separation is reduced, the wave function is altered since the system of two electrons of opposite spin feels the electrostatic potential of both protons. For example in the case of the Helium atom we apply the above equation for Z = 2 and get E = - 79 eV However in the case of the hydrogen molecule the detailed experiments showed that the separation of the two protons is ro = 0.74/1010 m which yield a positive potential Epp in eV given by Epp = Ke/ro = 14.4/0.74 = 19.46 eV In this case the system of two electrons of opposite spin feels not the electrostatic potential of the charge Ze = 2e but the potential of the effective charge ζe where 1 < ζ < 2. Thus we write E = -27.2 ζ2 +16.95 ζ - 4.1 + 19.46 eV Since the detailed calculations of the experiments yield E = -31.68 eV we may write 27.2 ζ2 -16.95ζ - 47.04 = 0. Then solving for ζ one gets ζ = 1.663. Nevertheless under the strong influence of the so-called Exchange Interaction today many physicists continue to believe that the molecular binding is a result of qualitative approaches. For example in the “Hydrogen molecule-HyperPhysics” one reads: “The classic case of covalent bonding, the hydrogen molecule forms by the overlap of the wavefunctions of the electrons of the respective hydrogen atoms in an interaction which is characterized as an exchange interaction. The character of this bond is entirely different from the ionic bond which forms with sodium chloride, NaCl. If you measure then energy balance when you form H+ and H- ions and examine the attractive force between them, the energy required is positive for any value of ion separation. That is, there is no distance at which there is a net attractive interaction, so the bond cannot be ionic. The electron distribution around the protons of the hydrogen is described by a quantum mechanical wavefuntion, and the wavefunction which describes the two electrons for a pair of atoms can be symmetric or antisymmetric with respect to exchange of the identical electrons. From the Pauli exclusion principle, we know that the wavefunctions for two identical fermions must be antisymmetric. The electron spin part of the wavefunction can be symmetric (parallel spins) or antisymmetric (opposite spins), but then the space part of the wavefunction must be the opposite. That gaurantees that the entire wavefunction (the product of the spin and space wavefunctions) is antisymmetric.” CONCLUSIONS The successful discovery of the electron spin which gives a peripheral velocity greater than the speed of light under the influence of the invalid relativity led to the abandonment of the well-established laws of electromagnetism. Note that the well-established laws of Coulomb and Newton were applied for the enormous success of the Bohr model and the Schrodinger equation. (See my BOHR AND SCHRODINGER REJECT EINSTEIN and HYDROGEN MOLECULE BINDING OF LAWS ). In fact. the peripheral velocity (u >> c) of spinning electrons gives a magnetic attraction of short range between the two electrons of opposite spin which overcomes the electric repulsion of long range at a short inter-electron separation. So the two electrons behave like one particle circulating about the two nuclei under the rules of quantum mechanics. However this situation of two coupling electrons leads to the vibration energy Ev = 16.95 ζ – 4.1. Also the two separated protons yield a positive energy of 19.46 eV . Nevertheless the total energy of -31.68 eV for ζ = 1.663 is stronger than the energy of -14.35 eV for Z = 1. Therefore compared to the original atomic orbitals, the bonding molecular orbital has lower energy and is therefore more stable. Category:Fundamental physics concepts